Simplify (10c^6d^-5)(2c^-5d^4)

$(10 c^{6} d^{- 5}) (2 c^{- 5} d^{4})$

Step 1

Multiply $c^{6}$ by $c^{- 5}$ by adding the exponents.

Move $c^{- 5}$ .

$10 (c^{- 5} c^{6}) d^{- 5} (2 d^{4})$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$10 c^{- 5 + 6} d^{- 5} (2 d^{4})$

Add $- 5$ and $6$ .

$10 c^{1} d^{- 5} (2 d^{4})$

Step 2

Simplify $10 c^{1} d^{- 5} (2 d^{4})$ .

$10 c d^{- 5} (2 d^{4})$

Step 3

Multiply $d^{- 5}$ by $d^{4}$ by adding the exponents.

Move $d^{4}$ .

$10 c (d^{4} d^{- 5}) \cdot 2$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$10 c d^{4 - 5} \cdot 2$

Subtract $5$ from $4$ .

$10 c d^{- 1} \cdot 2$

Step 4

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$10 c \frac{1}{d} \cdot 2$

Step 5

Multiply $10 c \frac{1}{d}$ .

Combine $10$ and $\frac{1}{d}$ .

$c \frac{10}{d} \cdot 2$

Combine $c$ and $\frac{10}{d}$ .

$\frac{c \cdot 10}{d} \cdot 2$

Step 6

Move $10$ to the left of $c$ .

$\frac{10 \cdot c}{d} \cdot 2$

Step 7

Multiply $\frac{10 c}{d} \cdot 2$ .

Combine $\frac{10 c}{d}$ and $2$ .

$\frac{10 c \cdot 2}{d}$

Multiply $2$ by $10$ .

$\frac{20 c}{d}$